value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Multiplication example, Example  Multiply 3x 5 + 4x 3 + 2x - 1 ...

Example  Multiply 3x 5 + 4x 3 + 2x - 1 and x 4 + 2x 2 + 4. The product is given by 3x 5 . (x 4 + 2x 2 + 4) + 4x 3 . (x 4 + 2x 2 + 4) + 2x .

Augmented matrix, Consider the following system of linear equations. X 1...

Consider the following system of linear equations. X 1 +x 3 +x 4 = 2 X 1 +x 2 +x 3 = 6 X 2 +x 3 +x 4 = 3 X 1 +x 2 +x 4 = 0  (a) Write out the augmented matrix fo

Find area of y = 2 x2 + 10 and y = 4 x + 16, Find out the area of the regio...

Find out the area of the region bounded by y = 2 x 2 + 10 and y = 4 x + 16 . Solution In this case the intersection points (that we'll required eventually) are not going t

Numerical analysis and computer techniques, write a fortan programme to gen...

write a fortan programme to generate prime number between 1 to 100

Prove that sec2+cosec2 can never be less than 2, Prove that sec 2 θ+cosec 2...

Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans:    S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot

What is box-and-whisker plot, Q. What is Box-and-Whisker Plot? Ans. ...

Q. What is Box-and-Whisker Plot? Ans. Line graphs or stem-and-leaf plots become difficult to manage when there is a large amount of data. Box-and-whisker plots help summa

Help, sin(x)+cos(x)

sin(x)+cos(x)

Limits at infinity, Limits At Infinity, Part I : In the earlier section w...

Limits At Infinity, Part I : In the earlier section we saw limits which were infinity and now it's time to take a look at limits at infinity.  Through limits at infinity we mean

Normal Distribution, You don''t have to give me the answer. I just want to ...

You don''t have to give me the answer. I just want to know HOW to do it. In a set of 400 ACT scores where the mean is 22 and the standard deviation is 4.5, how many scores are ex

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd